One interesting extension of the proposed method is optimizing a specific quantile of the survival distribution such as the median survival time.
However, this task introduces a unique challenge with respect to the backward recursion. Specifically, the optimal decisions made for later stages may not be optimal once earlier decisions moderate the distribution. Thus, an exhaustive search may be needed to find an optimal policy. An extension of the quantile-optimal dynamic treatment regime estimators developed by [1]} and [2]} to right-censored data would be interesting future work.
